Q2 observation position (median) in a sorted data set.

• A. n th observation
• B. 2(n+1)/4 th observation
• C. (n+1)/4 th observation
• D. (n+3)/4 th observation

Answer: (B)

The median is the middle value in a sorted list, so its position is the central index. For a dataset with n observations, the middle index is (n+1)/2. Writing it as 2(n+1)/4 is just another way to express the same thing, since 2(n+1)/4 simplifies to (n+1)/2. This matches the idea of a central position: when n is odd, it points to the exact middle observation; when n is even, there isn’t a single middle observation and the median comes from the two central positions at n/2 and n/2 + 1, with the central region centered around (n+1)/2. The other expressions don’t land at the center of the ordered list, so they aren’t the median position.